High school mathematics compulsory collection knowledge points
I. Collection of related concepts
The meaning of 1. set
2. Three characteristics of elements in a set:
The certainty of (1) element is as follows: the highest mountain in the world.
(2) The mutual anisotropy of elements, such as the set of happy letters {H, a, p, Y}.
(3) The disorder of elements: for example, {a, b, c} and {a, c, b} represent the same set.
3. Representation of set: {? Such as: {Basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean, Arctic Ocean}
(1) The set is expressed in Latin letters: A={ basketball players in our school}, B={ 1, 2, 3, 4, 5}.
(2) Representation methods of sets: enumeration method and description method.
U note: commonly used number sets and their symbols:
The set of nonnegative integers (i.e. natural number set) is recorded as n.
Positive integer set N* or N+ integer set z rational number set q real number set r
1) enumeration method: {a, b, c}
2) Description: A method of describing the common attributes of elements in a collection and writing them in braces to represent the collection. {x？ r | x-3 & gt； 2}，{ x | x-3 & gt； 2}
3) Language description: Example: {A triangle that is not a right triangle}
4, the classification of the set:
The (1) finite set contains a set of finite elements.
(2) An infinite set contains an infinite set of elements.
(3) An example of an empty set without any elements: {x | x2 =-5}
Second, the basic relationship between sets
1.？ Contain? Relationship? subset
note:
There are two possibilities that A is a part of B (1); (2)A and B are the same set. On the other hand, set A is not included in set B, or set B does not include set A and is recorded as AuB or BuA.
2.？ Equality? Relationship: A=B (5? Five plus five? 5, then 5=5)
Example: suppose a = {x | x2-1= 0} b = {-1,1}? If the elements are the same, are the two sets equal?
Namely: ① Any set is a subset of itself. Answer? A
② proper subset: If a? B and a? B then says that set A is the proper subset of set B, and it is denoted as AuB (or BuA).
3 if a? B，B？ C, then a? C
4 if a? At the same time? Then A=B
3. A set without any elements is called an empty set, and it is recorded as?
It is stipulated that an empty set is a subset of any set and an empty set is a proper subset of any non-empty set.
U has a set of n elements, including 2n subsets and 2n- 1 proper subset.
?